This invention relates generally to beam forming apparatus and more particularly to beam forming apparatus adapted to form beams having shapes in accordance with signals received by the apparatus from an environment having both desired signal sources and undesired noise or interfering signal sources.
As is known in the art, beam forming apparatus are used to form beams of sonic or electromagnetic radiation. The shape of the beam is related to the phase and amplitude distributions provided to signals received across an aperture of the apparatus. One type of beam forming apparatus is adapted to sense the received signals incident across the aperture and then adjust the phase and amplitude of such received signals in accordance with some desired performance criterion, such as maximization of the received signal-to-noise ratio. Such apparatus may thus be considered as an adaptive beam forming apparatus, and, when used in radar systems, such apparatus is generally referred to as an adaptive antenna as discussed in a book entitled Introduction to Radar Systems by Merrill I. Skolnick (second edition), published by McGraw-Hill Book Company, 1980, Page Nos. 332 and 333. Additional discussions of adaptive arrays are presented in an article entitled "Adaptive Arrays - An Introduction", by William F. Gabriel, published in the "Proceedings of the IEEE", Volume 64, No. 2, February 1976, Page Nos. 239-272. In such article, it is pointed out that an adaptive array is a system having an array of antenna elements and a real-time adaptive receiver processor which, given a beam steering command, samples its current environment and then automatically proceeds to adjust its element control weights towards optimization, usually to maximize the output signal-to-noise ratio. The noise may consist of deliberate electronic counter-measures, friendly radio frequency interference, clutter scatter returns, and natural noise sources. One technique suggested for adaptively optimizing the signal-to-noise ratio is discussed in a paper entitled "Adaptive Array" by Sidney P. Applebaum published in the "IEEE Transactions on Antennas and Propagation", Volume AP-24, No. 5, September 1976. Maximization of the signal-to-noise ratio is achieved when signals received by the antenna elements are weighted in accordance with the equation: W=.mu.M.sup.-1 S*, where W is a matrix of the weighting factors to be applied to the received signals at the antenna elements; M is the covariance matrix of the noise component of the received signals; .mu. is an arbitrary constant; and, S* is the complex conjugate of the phase distribution of the desired signal to be detected across the array elements. The article uses this equation and applies it to a linear, uniformly spaced array of antenna elements. It is assumed that in the quiescent environment, the noise outputs of the antenna elements have equal powers. The noise environment studied is that of a single jammer added to the quiescent environment. The desired signal is assumed to be at an angle .theta..sub.s from the mechanical boresight, while the jammer is assumed to be at an angle .theta..sub.j from the mechanical boresight. The author then shows that the beam or radiating pattern resulting from applying weights in accordance with the aforementioned equation consists of two parts: the first is the quiescent pattern (that is the pattern which would be produced by the apparatus in the absence of the jammer; one with the main lobe pointing in the direction of the desired signal, i.e., at angle .theta..sub.s); and, the second, which is subtracted from the quiescent pattern, is a (sin Kx/sin x) shaped beam centered on the jammer, where K is the number of antenna elements in the array and x is related to the angle from boresight. As a result of weighting the signals received by the antenna elements in accordance with the equation, the gains of both the first and second part of the resulting beam are equal to each other at the jammer angle .theta..sub.j. The result of the subtraction of the two parts therefore is a resulting beam having a substantial null in the direction of the jammer, that is, at the angle .theta..sub.j. It should be noted that with this technique, weighting factors must be computed for each of the signals produced at each of the antenna elements, a relatively complex signal processing problem. A technique described which enables rapid convergence of the solution to the aforementioned equation is described in an article entitled "Rapid Convergence Rate in Adaptive Arrays" by I. S. Reed, J. D. Mallett and L. E. Brennan, published in the "IEEE Transactions on Aerospace and Electronic Systems", Volume AES-10, No. 6, November 1984, Page Nos. 853-863. The technique described therein is referred to as "Sample Matrix Inversion" (SMI). With such technique, an estimate is made of the covariance matrix M using S samples. Next, the estimated M of M is inverted, finally, the filter M.sup.-1 S* is formed. While the SMI technique does result in a more rapid convergence in the solution of the Appelbaum equation such technique sometimes produces a resulting beam having relatively poor antenna side lobes when applied to arrays having a reasonable number of antenna elements.